Finite Group Databasebeta

← #20242357

Subgroups — #20242357

Order 6016.

282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689261C212yesmaximal, complemented
2#15689043C211yesmaximal, characteristic, complemented
3#15688857C212yesmaximal, complemented
4#15688849C211yesmaximal, characteristic, complemented
5C47×#537C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C2×#10625335—22no—
8C2×Dic47⋊C4—21no—
9#13093947—22no—
10C22⋊(C47⋊C8)C2212yes—
11C47⋊#95—21no—
12C47⋊#95C2211yescharacteristic
13C2×#41×C47—21no—
14C22⋊Q8×C47—22no—
15#121×C47—22no—
16#121×C47—21no—
17#121×C47C2212yes—
18C2×C4⋊C4×C47C2211yescharacteristic
19#41×C47—42no—
20#41×C47—42no—
21C2×Q8×C47—21no—
22C2×D4×C47—21no—
23C2×D4×C47—22no—
24C2×D4×C47—21no—
25C2×D4×C47D412yes—
26C22×C4×C47—22no—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C2×Dic94—22no—
33C2×Dic94—42no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—22no—
36C4⋊C4×C47D412yes—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39#10625335—44no—
40Dic47⋊C4—42no—
41C2×C47⋊C8—22no—
42C23×C47—22no—
43C23×C47C2×D411yescharacteristic
44Q8×C47—42no—
45D4×C47—42no—
46D4×C47—42no—
47D4×C47—42no—
48D4×C47—42no—
49D4×C47—81no—
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47—44no—
56C2×C4×C47—41no—
57C2×C4×C47SD1612yescomplemented
58C2×C4×C47C2×D412yes—
59C2×Dic47—22no—
60C2×Dic47—22no—
61C2×Dic47—41no—
62C2×Dic47—41no—
63C2×Dic47—41no—
64C2×Dic47—41no—
65Dic94—24no—
66Dic94—42no—
67C47⋊C8—42no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47—42no—
71C22×C47—42no—
72C22×C47—42no—
73C22×C47#12011yescharacteristic
74C22×C47C2×SD1611yescharacteristic
75C22×C47AGL(1,ℤ/8)11yescharacteristic
76C4×C47—22no—
77C4×C47—22no—
78C4×C47—42no—
79C4×C47—41no—
80Dic47—42no—
81Dic47—42no—
82#1604—471nomaximal, Sylow
83C2×C47—21no—
84C2×C47—21no—
85C2×C47—82no—
86C2×C47#45011yescharacteristic
87C2×C47#45611yescharacteristic
88C2×C47B(4,𝔽2)11yescharacteristic
89#537D4711yescharacteristic
90#448—472no—
91#395—471no—
92#327—472no—
93#324—471no—
94C47#160411yescharacteristic, complemented, Sylow
95C2×#41—21no—
96C22×Q8—471no—
97C2×SD16—942no—
98C22⋊Q8—22no—
99#121—22no—
100#121—21no—
101#121C2×D4712yes—
102C2×C4⋊C4—941no—
103C2×C4⋊C4C2×D4711yescharacteristic
104#103—942no—
105C22⋊C8—472no—
106#95—471no—
107#95—941no—
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—942no—
112C2×Q8—1882no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D4712yes—
117C22×C4—22no—
118C22×C4—941no—
119C22×C4—941no—
120C22×C4C22⋊D4711yescharacteristic
121C22×C4C22⋊D4711yescharacteristic
122C22×C4C22×D4711yescharacteristic
123SD16—1884no—
124C2×C8—942no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—1882no—
128C4⋊C4C22⋊D4712yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D4711yescharacteristic
133Q8—42no—
134Q8—944no—
135Q8—1882no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—942no—
149C2×C4—942no—
150C2×C4—1881no—
151C2×C4—1881no—
152C2×C4—1881no—
153C2×C4—1881no—
154C2×C4#1062533512yescomplemented
155C2×C4C2×C22⋊D4712yes—
156C8—1882no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1309399311yescharacteristic
163C22C2×#1062533511yescharacteristic
164C22#1309405011yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—41no—
169C4—1882no—
170C4—1882no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1568927411yescharacteristic
175C2#1568930611yescharacteristic
176C2#1568931011yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#537C2
socleC22×C47#120
hypercenter#537D47
hypocenterC47#1604
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689261C2semidirect
2. #15689043C2semidirect
3. #15688857C2semidirect
4. #15688849C2semidirect
57. C2×C4×C47SD16semidirect
94. C47#1604semidirect
154. C2×C4#10625335semidirect